Well, we found out what your pet is really trying to tell you from animal therapist Warren Eckstein. Let's start with dogs:

What does it mean when you come home after work and your dog licks your face? It means he wants food not affection. Although your dog is happy to see you, the essence of his behavior is saying "Feed me!" This is something ingrained in domesticated dogs from their wild ancestors. Out in the wild, when the leader of the pack returned from a hunt, the other dogs would lick his face to taste his food. Of course, you're not returning from a hunt, but your dog doesn't know this.

Okay, well what does it mean when your dog yawns? Is he bored? Nope, he's stressed out. Yawning isn't natural for a dog so when they do it, they're stressed or upset about something. It can also be a displaced bite--A behavior they've adopted instead of biting. So what should you do when your dog yawns? Pet him. Studies show that being petted lowers your pet's heart rate and blood pressure which will reduce his stress.

Now, on to your cat. Why does she rub herself against your furniture? It's her way of saying 'I love you.' Cats instinctively rub each other to say hello and to show they like each other. But since you're not always around, your cat will rub herself against your furniture or anything else that smells like you.

Okay, one last one: Why does your cat drool when she sits on your lap? Because she feels safe with you. Your comforting lap reminds her of being safe with her mother and it triggers the same reaction a drooling reflex just like when your cat was a kitten and nursing.
If you'd like to know more, there are two books you should check out: "Good Owners, Great Cats" or "Good Owners, Great Dogs".